How can faces be added to a manifold mesh without losing the manifold property?
Non-manifold geometry basically occurs when you have an edge that is part of more or less than exactly two faces. For the sake of 3D printing this is important because non-manifold geometry is geometry that isn't describing the outer shell of a physical object. And edge that is connected to more than two faces means that you have faces that are 'inside' your mesh, for example.

Basically, if you add that face there, you need to delete some of your older geometry that is becoming internal. I'm not 100% sure this is what you're trying to accomplish, but it should give you the basic idea:



Delete faces that would become 'inside' faces, then select the edge loops around the hole you've created, and fill them. It's possible that you will want to clear away one more faces. As I've done it above, you have a hex shaped indent both inside and outside the cylinder. The same technique works if you want a smooth cylinder on the inside.